It is interesting to note that while FDTD is based on Maxwell’s equations which describe the behavior and effect of electromagnetism, the term “FDTD” itself was coined to describe the algorithm developed by Kane S. Yee in computational electromagnetism. Maxwell’s equations were based on the work of James Clerk Maxwell, a Scottish mathematician who published its initial form in 1861. Yee, born in China but acquired PhD Applied Mathematics from the University of California in Berkely, described his algorithm in 1966.
Prior to the Yee algorithm, FDTD had been used to solve problems in computational fluid dynamics. In Yee’s work, he suggested a novel way of applying FDTD operators on staggered grids for each of the vector field components in Maxwell’s equations. However, the term finite-difference time-domain (FDTD) itself was coined in by a professor Allen Taflove from the Northwestern University’s McCormick School of Engineering located in Illinois. He had published a paper on the August 1980 IEEE Trans. Electromagnetic Compatibility issue entitled “Application of the finite-difference time-domain method to sinusoidal steady-state electromagnetic penetration problems.”
It was only in 1990 that FDTD techniques became popular in dealing with problems concerning interactions of electromagnetic waves, mostly because of the rise of wireless communication devices, but it is also used to model applications in the fields of geophysics and biomedical imaging and the convenience of computers equipped with fast processors and large memories. There are numerous developers for FDTD application software, including at least 27 which are proprietary, 8 which are open access, and two freeware.
The finite-difference time dimension (FDTD) method for simulating computational electromagnetism is considered the simplest and most efficient way to model the effects of electromagnetism on a certain material or object. The most commercial use of the FDTD model is in mobile communication systems, which makes use of radio frequencies, so engineers have to be able to project how the device will most likely operate in the real world by running simulations. Another application for FDTD is in fiber optics, which is also a technology that relates to communication, and there is an increasing interest in its use in nanotechnology. In a very real way, the FDTD method is used to design and improve the mobile and fixed communication technology we have today.
In terms of scalability, the FDTD method proves robust, merely requiring additional time to do the computation with no changes in the formula. However, while it is a relatively simple method, it requires fine grids to develop a model. FDTD does require a lot of computations which increase exponentially with the number of elements. In order to do an FDTD model, one will require a powerful computer with a lot of memory. It is recommended that a computer running a graphical processing unit (GPU) processor, which is specifically designed to handle large amounts of graphical data in parallel, which is exactly what is needed. How long it takes to complete a simulation will depend on the number of elements in an FDTD simulation and processing speed of the computer. In general, an FDTD model requires 30 bytes of memory per Yee cell and 80 operations per cell, per time step.
Suffering injuries in a truck accident can be a devastating experience to go through. The fact of the matter is that truck accident victims are rarely in a position to be able to afford the costs of medical treatment, loss of income, or other expenses that they may have to deal with as a result of their injuries. For this reason, truck accident victims are often in a position where pursuing compensation from those responsible for their injury may be the only way to get their lives back together.
A recent case from Texas illustrates the ways in which a personal injury suit for truck accident damages can help those whose lives have been impacted by this type of situation. The family of Daniel Rhodes, who died in a truck accident in 2011, was represented by attorney Jim Hart of the Williams Kherkher law firm in Houston, Texas. Hart was able to successfully argue that the companies for which the driver of the truck was working had failed to train him properly, leading to the tragic loss of Daniel Rhodes’ life after the truck driver attempted a dangerous maneuver in trying to return to the road.
The jury in the case found in favor of the plaintiffs and awarded a total of damages in the amount of $11 million, though the two parties afterwards settled out of the court for an undisclosed sum. Nevertheless, this case illustrates how critical the role of a qualified legal professional can be in helping the victims of truck accidents to fight for justice.
Electromagnetism is a fundamental force in nature that establishes the internal properties of all things on Earth. It is a phenomenon that is manifested in the interrelationship between electricity and magnetism, and the interaction of electrons and photons at the atomic and molecular level. The theory confirms that one can be produced by the other and also explains the nature of light.
Electromagnetism is a relatively modern concept. Prior to the 19th century, scientists believed that magnetism and electricity were distinct forces. It was not until scientists from Denmark (Hans Christian Ørsted), France (André-Marie Ampère) and England (Michael Faraday) worked out the dynamics that inextricably linked electricity and magnetism that the idea it was a single force piqued scientific interest. This was formally synthesized in 1865 into the electromagnetic theory by Scottish mathematician and physicist James Clark Maxwell, who had been tasked to transcribe Faraday’s experiments in electricity and magnetism into mathematical terms.
In his set of equations, Maxwell demonstrated that electricity and magnetism traveled in distinct waves through space, and that light itself is the result of the undulations of the electromagnetic waves which travelled at the same velocity as light. Together, electricity, magnetism, and light comprise the electromagnetic field.
However, Maxwell’s publication only became accepted outside of England when Heinrich Hertz, a German physicist, verified his equations in 1886. To add insult to injury, it was only in 1905 when the Theory of Relativity proposed by Albert Einstein that it cemented the notion that electricity and magnetism were two sides of the same coin, although they are by no means the same force.
The significance of the electromagnetic theory is that it became the basis for many of the theories in advanced physics, including quantum mechanics, which speculates on the properties of nano particles in relation to the physical world. Because these particles are so small, they can only be detected by how it affects the electromagnetic field.
The fact of the electricity and magnetism interrelationship being discovered to give way to electromagnetism is hugely relevant when it comes to practical applications in modern life. True, it is the basis for the nebulous and largely theoretical worlds of quantum physics and quantum mechanics, but the fact is for most people it is what makes the world go around.
The basic principle behind how electromagnetism is generated is the core concept of household electricity. The fact that we can turn the power on and off at will is a convenience that we all take for granted but is actually a crucial part of modern living. Because an electromagnetic field produces the energy that makes any gadget or appliance work, its continued presence is necessary to keep the machine or motor going. It is only through the passing of an electrical current that this electromagnetic field can be generated, the modern householder can control when that field is produced by simply flipping a switch. This in turn cuts off or supplies the electrical current that drives the electromagnetic field. Voila! Power at the flick of a finger!
Gadgets that make use of electromagnetism exploit the fact that the flow of electricity dictates when the magnetic field is energized, thus having control of this flow makes the gadget work as needed. An electromagnet is typically constructed of an iron core with a conductor such as copper wound around it which will carry the current that will activate the magnetic field. The strength of the field will depend on the amount of current that passes through the copper coil. A good example would be those large magnets that move heavy metal objects around a junkyard. An electric current energizes the magnet, causing metal to get attracted so that they can be moved. Once the object is in position, the electric current is cut off, causing the magnet to de-energize and release the object.
Common household appliances also use electromagnetism to work, such as televisions, electric fans, door bells, electronic door locks, loudspeakers, audio and video tapes, computers, and storage devices. Mobile phones would not be possible without electromagnetic pulses to carry the signals, and in the medical field, it is used in diagnostic equipment such as the Magnetic Resonance Imaging (MRI) scans. Electromagnets are also used for magnetic levitation (Maglev) trains.
These are just a few of the more obvious uses of electromagnetism. With technology and science developing at lightning speeds, it is entirely possible that there will be more uses for electromagnetism in the future. Right now, it is a crucial part of daily life.
Perhaps one of the more interesting movies electromagnetically speaking is The Core. The basic premise of the movie is that the Earth’s outer core, supposedly the third layer of what makes up the planet, which is believed to be in constant motion, has stalled due to human interference. As a result, the electromagnetic field that surrounds the earth protecting it from the destructive power of the Sun’s cosmic rays has become unstable, creating earthquakes, electrical failure, and general breakdown of basic electronic technology, including pacemakers. The disruption has also caused birds to lose their sense of direction and sends them careening into stone statues to die in front of small children in parks. The mission of the protagonists is to jump start the planet by detonating a series of nuclear bombs at strategic points in the liquid iron of the outer core.
The Earth does have a protective magnetic field around it that protects the surface from being inundated by powerful solar rays that can cause, at the least, serious personal injury from radiation. An electromagnetic field is generated from the motion of charged particles, and in the case of the outer core, it is the extremely high heat that sets the charged particles in motion. It is also true that this continuous motion of the liquid metal in the outer core does generate this protective field, which extends to about 78 miles up from the crust (surface of the Earth). Occasionally, fluctuations in the field lets in more cosmic rays than usual, affecting communications, power grid networks, and satellite reception, which was demonstrated in the first part of the movie.
It should be noted there are some points in the movie that reeks of bad science, such as the existence of amethysts in the mantle, which is in turn posited to be mostly empty space. While scientists have yet to penetrate to the mantle, known scientific facts make these suggestions highly improbable. However, the movie does base most of its propositions on sound principles, save for the fact that the motion of outer core could be stopped or restarted with existing technology.
There has been a growing concern that because of the proliferation of electrical and electronic gadgets, humans have become more frequently exposed to electromagnetic fields (EMF) at dangerous levels. Reports of increased incidence of anxiety, headaches, decreased sexual appetite, nausea and fatigue have been suggested to have been caused by long-term EMF exposure in the home. These include such homely accoutrements as televisions, microwave ovens, cable, computers, radars, and mobile phones as well as power lines and nuclear power plants.
In general, the average person is exposed to constant doses of low-frequency, non-ionizing EMFs, and there is no evidence to suggest that this has an adverse cumulative effect on the health. The body itself runs on tiny bursts of electrical current resulting from biochemical reactions natural to normal bodily functions.
This is of course a lot lower than the electric current that runs through a construction site worker who accidently touches an exposed live wire, which can certainly pose a significant health threat. For the average person, however, constant low-frequency EMF exposure is generally safe, even when standing (without actual contact) beneath a high voltage power lines.
This bears special mention because there have been allegations that proximity to power lines increases the risk of developing childhood leukemia. Despite numerous studies into the matter (approximately 25,000 and counting), there has been no conclusive evidence that this is so, although it may be prudent to err on the side of caution and avoid prolonged exposure to these areas when possible.
This is not to say that EMFs have no effect on the human body. It induces currents to circulate and depending on how strong the magnetic field is can stimulate muscles and nerves and interfere with biological processes. Overall, however, the body is able to cope with EMF exposure provided it is at non-ionizing levels such as is found in normal everyday life.
An electromagnetic field or EMF is produced when a charged particle is accelerated or put in motion, typically with the introduction of an electrical current. Electrical fields can occur whether the charged particles are static or in motion, but a magnetic field is only produced when the charged particles are in motion, so to produce an EMF, there must be a current present.
As matter is made up of particles, it is possible to find an EMF anywhere in the environment. In fact, EMFs are constantly present all around us, but it is not visible. However, its effects can be observed, depending on two elements: frequency and wavelength.
Frequency is defined as the number of waves generated in a second while wavelength is the measurement from one wave to the next, which depends solely on the frequency. The more waves generated in a second or higher frequency the smaller the distance between waves or shorter wavelength. The different EMF forms are defined by a specific frequency and wavelength, which also determines if they are ionizing or non-ionizing EMFs.
EM waves produce energy. They are carried along by particles referred to as quanta (singular quantum), and high frequency EM waves generate more energy than low frequency waves. When an EMF generates enough energy, it can break the chemical bonds that hold molecules together, and these are called ionizing EMFs. Radioactive materials typically produce ionizing EMFs when they are accelerated, such as gamma rays and X-rays. This is why X-ray technicians don protective clothing, to prevent injury from operating X-ray machines.
EMFs occur naturally, primarily as a result of thunderstorms, which would account for the charged feeling in the air when lightning strikes. They are also generated from man-made objects such as electrical appliances and communication equipment. Lower frequency EMFs that are not strong enough to break bonds between molecules are non-ionizing EMFs, and these include radios, microwaves, and electrical household equipment.
There are numerous ways to solve problems in computational electromagnetics. While all are feasible, one method has seen a meteoric rise in popularity since its inception in 1966: the finite-difference time-domain method (FDTD).
FDTD is a method of solving problems in computational electromagnetics that uses Maxwell’s equations and derivations of them to illustrate the behavior of electromagnetic fields around an object. In these equations, space and time are combined into spacetime, rather than examined as two separate entities. This means that in a FDTD problem, for any given moment in time, there is only one possible arrangement of the electromagnetic fields surrounding an object.
The finite-difference time-domain method compares the change in an electronic field in time against a change in a magnetic field across space. Conversely, it also examines the changes in a magnetic field along an analogous electronic field in space. By incrementally stepping through individual moments in time while measuring the strengths of electromagnetic fields along the space, the FDTD method creates a model of the electromagnetic fields acting on an object.
The FDTD method is performed on a given space and equations are elegant enough to account for the properties of the materials being examined, such as their electrical conductivity, permittivity, and permeability. When put through a computer, the method essentially runs a simulation of the electromagnetic fields of an object. This creates a lot of data that can be mined and visualized. It’s even possible to simulate the effects of the addition of an electromagnetic pulse to the model, making the method invaluable to engineers working with antennae and other electromagnetic receivers.
While FDTD has gained a lot of popularity for its intuitiveness and ability to outline huge models as they change through time, it does have its drawbacks. FDTD requires a great deal of preparatory planning on the system. It calls for every aspect of the item upon which the simulation is to be run to be modeled at a degree precise enough to account for tiny differences in electromagnetic wavelengths. FDTD may also take more computing time than other methods, especially depending on the shape of the object being examined.
The Future Data Testing Department uses this method as well as others in its data acquisition, visualization, and machine learning projects. Of course, this is nowhere near a full discussion of the complexities of the finite-difference time-domain method, but we believe it’s a reasonable overview of how and why we employ it.
Computational electromagnetics, also known as electromagnetic modeling, is a fascinating study that helps scientists visualize the activity of electromagnetic waves on a given object. In computational electromagnetics, scientists use computers to solve, or at least approximate, solutions to Maxwell’s equations, mathematical formulas that describe the behavior of electric fields, magnetic fields, charges, and currents. They are a fundamental part of many areas of scientific study and advancement, including circuitry, and optics.
For computational electromagnetics, these equations are used to model the way an electromagnetic field will behave around an object. Prepared Maxwell’s equations are fed into supercomputers, though the systems are usually so complex that in most cases they aren’t completely solved, but rather approximated. This complexity arises from the number of iterations of complicated mathematical functions the computer has to perform in order to return a result. In order to get an accurate model, electromagnetic fields must be calculated for multiple instances in time, across numerous points, taking into account each possible interference or interaction. Because electricity and magnetism are linked, this is a daunting task, even for a supercomputer.
Computational electromagnetics is often used while designing communications technologies. For example, an engineer may be designing an antenna or other wireless receiver. These receivers function by detecting changes in electromagnetic waves, so it’s vital for the person designing them to be aware of how their devices interact with and create electromagnetic fields. Using computational electromagnetics practices, our friendly engineer can have an accurate visualization of the electromagnetic fields that would exist in his design.